1. 9.1 Similar Right Triangles
Unit IIB Day 2

2. Do now:
Write a similarity statement.
ACB ~ CDB ~ ADC

3. If you set up proportions, what do you notice about the relationship of CD (the altitude) to the other side lengths?

4. Geometric Mean Theorems
Note: Altitude splits hypotenuse into two parts.
Theorem 9.2: The length of the altitude is the geometric mean of the lengths of the two parts of the hypotenuse. BD CD = AD

5. Geometric Mean Theorems
Theorem 9.3: The length of each leg of the right triangle is the geometric mean of the lengths of the whole hypotenuse and the adjacent part of the hypotenuse. AB AC = AD AB CB = DB

6. Ex. 2: Geometric Mean Theorems
Find the value of the variable.
6/x = x/3
x = sqrt(18)
y/2 = 7/y
y = sqrt(14)

7. Ex. 3: Using Indirect Measurement.
To estimate the height of a monorail track, your friend holds a cardboard square at eye level. Your friend lines up the top edge of the square with the track and the bottom edge with the ground. You measure the distance from the ground to your friends eye and the distance from your friend to the track. Find the height,
h = XZ.
In the diagram, XY = h – 5.75 is the difference between the track height h and your friend’s eye level. Use Theorem 9.2 to write a proportion involving XY. Then you can solve for h.
xy/wy = wy/zy — geometric mean thm 1
(h – 5.75)/16 = 16/5.75 — substitute
h = about 50 feet

8. More Examples
Complete the proportion. Then solve for x.

9. More Examples
Find the value of the variable.
a) b)